In the mid-left are the players and some of their stats.
Clicking a "View" link causes details to be displayed at the top. The player viewed takes center stage. The opponent that the player gives a tunnel segment to is on the left. The opponent who gives the player a tunnel segment in on the right. Pickaxes mark those working in tunnels. Swords mark those fighting for their segments back. The viewed player has both.
Each of these four sections has a table displaying the total power of each of its factions versus an opposing faction. The factions and power modifications of the individual cards will be listed below, but they can largely be ignored. The extra columns are for card effects. (This is the first turn so there aren't any cards listed yet.)
Pickaxes also mark the two tunnels involved. The tunnel symbols (diamonds and shovels) of the cards forming the tunnel will be listed underneath.
Phase directions are given in the middle of the screen. In the mid-right are a player's cards. Unlike the top section, each card displays all of its stats. The far left and right columns offer boxes which can be clicked to select a card. Above the column is an icon representing where the selected card will go. (The phase in the above screenshot only involves a single card so only one column is offered.)
...In other words, the only thing a player has to do during any phase is choose whether or not to select cards in the left or right column based on the information at the top of the screen.